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for this workshop

Arithmetic reflection groups and crystallographic packings

March 16 to March 20, 2020

at the

American Institute of Mathematics, San Jose, California

organized by

Alex Kontorovich, Alice Mark, and Daniel Allcock

This workshop, sponsored by AIM and the NSF, will be devoted to the complete classification of maximal hyperbolic arithmetic reflection groups. About 15 years ago, the number of such groups was shown to be finite, leaving open the possibility of fully determining all of them, in a way that makes them accessible for other applications, e.g., to the study of crystallographic sphere packings. Recent advances, both theoretical and algorithmic, make it plausible that with sufficient collaborative effort by experts in diverse areas from geometry/topology, dynamics, arithmetic groups, and number theory, we will be able to complete this program.

The main topics of the workshop are:

  • Restricting the search space by, on one hand combinatorial and geometric methods, and on the other, spectral gap (Ramanujan) methods
  • Computation methods in arithmetic groups
  • Vinberg-type and related algorithms

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than September 16, 2019. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.

Before submitting an application, please read the description of the AIM style of workshop.

For more information email

Plain text announcement or brief announcement.